On $p$-convexification of the Banach-Kantorovich lattice
Let $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. Let $(E,\|\cdot\|_{E}) \sub...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
EJAAM
2024-12-01
|
| Series: | E-Journal of Analysis and Applied Mathematics |
| Subjects: | |
| Online Access: | https://ejaam.org/articles/2024/10.62780-ejaam-2024-004.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1823864943596797952 |
|---|---|
| author | Gavhar B. Zakirova |
| author_facet | Gavhar B. Zakirova |
| author_sort | Gavhar B. Zakirova |
| collection | DOAJ |
| description | Let $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. Let $(E,\|\cdot\|_{E}) \subset C_\infty (Q(B))$ be a Banach-Kantorovich lattice over the algebra $L^0(\Omega)$ of equivalence classes of almost everywhere finite real-valued measurable functions on a measurable space $(\Omega, \Sigma, \mu)$ with $\sigma$-finite measure $\mu$. The paper defines the $p$-convexification of the Banach-Kantorovich lattice $(E,\|\cdot\|_{E})$ and proves that it is also a Banach-Kantorovich lattice over $L^0(\Omega)$. |
| format | Article |
| id | doaj-art-e35b5a82f2704a41aa37addd447c3f12 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-e35b5a82f2704a41aa37addd447c3f122025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902024-12-01202410.62780/ejaam/2024-004On $p$-convexification of the Banach-Kantorovich latticeGavhar B. Zakirova0Tashkent State Transport University, 1, Temiryolchilar street, Tashkent, 100167, UzbekistanLet $B$ be a complete Boolean algebra, $Q(B)$ the Stone compact of $B$, and let $C_\infty (Q(B))$ be the commutative unital algebra of all continuous functions $x: Q(B) \to [-\infty, +\infty]$, assuming possibly the values $\pm\infty$ on nowhere-dense subsets of $Q(B)$. Let $(E,\|\cdot\|_{E}) \subset C_\infty (Q(B))$ be a Banach-Kantorovich lattice over the algebra $L^0(\Omega)$ of equivalence classes of almost everywhere finite real-valued measurable functions on a measurable space $(\Omega, \Sigma, \mu)$ with $\sigma$-finite measure $\mu$. The paper defines the $p$-convexification of the Banach-Kantorovich lattice $(E,\|\cdot\|_{E})$ and proves that it is also a Banach-Kantorovich lattice over $L^0(\Omega)$.https://ejaam.org/articles/2024/10.62780-ejaam-2024-004.pdfp-convexificationmaharam measurebanach-kantorovich space |
| spellingShingle | Gavhar B. Zakirova On $p$-convexification of the Banach-Kantorovich lattice E-Journal of Analysis and Applied Mathematics p-convexification maharam measure banach-kantorovich space |
| title | On $p$-convexification of the Banach-Kantorovich lattice |
| title_full | On $p$-convexification of the Banach-Kantorovich lattice |
| title_fullStr | On $p$-convexification of the Banach-Kantorovich lattice |
| title_full_unstemmed | On $p$-convexification of the Banach-Kantorovich lattice |
| title_short | On $p$-convexification of the Banach-Kantorovich lattice |
| title_sort | on p convexification of the banach kantorovich lattice |
| topic | p-convexification maharam measure banach-kantorovich space |
| url | https://ejaam.org/articles/2024/10.62780-ejaam-2024-004.pdf |
| work_keys_str_mv | AT gavharbzakirova onpconvexificationofthebanachkantorovichlattice |